A B C 
Homework

Problem C2

The ratios seem to be approaching one number, which is about 1.618, to three decimal places.

<< back to Problem C2

Problem C3

If the pattern continues, this ratio should be fairly close to the ratios found in the table in Problem C2; it should also be very close to the ratio of the other consecutive Fibonacci numbers around it.

<< back to Problem C3

Problem C4

Consider the ratio of sides in each golden rectangle. In Rectangle 1, the ratio is ø to 1. In Rectangle 1 + 2, the ratio is ø + 1 to ø. These are similar rectangles, so the ratios must be equal:

Cross-multiplying and simplifying the equation gives us a quadratic equation: ø² - ø - 1 = 0. This equation does not factor, so we must use the quadratic formula to find the value of ø; the two possible values are

.
Since the side of a rectangle can't be negative,

.

Evaluating this on a calculator gives us the decimal 1.618 to three decimal places, as expected.

<< back to Problem C4

Home | Catalog | About Us | Search | Contact Us | Site Map

Tweet |

© Annenberg Foundation 2013. All rights reserved. Privacy Policy